library(readr)
data <- read_csv("data/new_data/data_bystate_temp_perc.csv")
Rows: 1334 Columns: 21── Column specification ─────────────────────────────────────────────────────────────────────────
Delimiter: ","
chr  (2): months, state
dbl (19): year, colony_n, colony_max, colony_lost, colony_lost_pct, colony_added, colony_reno...
ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
library(dplyr)

Attaching package: ‘dplyr’

The following objects are masked from ‘package:stats’:

    filter, lag

The following objects are masked from ‘package:base’:

    intersect, setdiff, setequal, union
data <- data %>% mutate(colony_lost_pct = colony_lost_pct/100)
data <- data %>% mutate(Varroa.mites = Varroa.mites/100)
data <- data %>% mutate(Other.pests.parasites = Other.pests.parasites/100)
data <- data %>% mutate(Disesases = Disesases/100)
data <- data %>% mutate(Pesticides = Pesticides/100)
data <- data %>% mutate(Other = Other/100)
data <- data %>% mutate(Unknown = Unknown/100)

LINEAR MODEL

lin_mod_n <- lm(data=data, colony_lost ~ colony_max + state + months + Varroa.mites +Other.pests.parasites+Disesases+Pesticides+Other+Unknown+year)
summary(lin_mod_n)

Call:
lm(formula = colony_lost ~ colony_max + state + months + Varroa.mites + 
    Other.pests.parasites + Disesases + Pesticides + Other + 
    Unknown + year, data = data)

Residuals:
   Min     1Q Median     3Q    Max 
-91795  -1468   -236   1542  67858 

Coefficients:
                        Estimate Std. Error t value Pr(>|t|)    
(Intercept)            4.429e+05  1.631e+05   2.715  0.00671 ** 
colony_max             1.613e-01  3.082e-03  52.326  < 2e-16 ***
statearizona           1.897e+02  1.726e+03   0.110  0.91250    
statearkansas         -1.105e+03  1.719e+03  -0.643  0.52028    
statecalifornia       -5.189e+04  3.977e+03 -13.046  < 2e-16 ***
statecolorado         -2.762e+02  1.750e+03  -0.158  0.87456    
stateconnecticut       2.131e+02  1.737e+03   0.123  0.90241    
stateflorida          -8.585e+03  1.881e+03  -4.565 5.48e-06 ***
stategeorgia          -3.632e+03  1.750e+03  -2.076  0.03813 *  
statehawaii            9.786e+00  1.814e+03   0.005  0.99570    
stateidaho            -8.695e+03  1.788e+03  -4.863 1.30e-06 ***
stateillinois         -2.443e+02  1.707e+03  -0.143  0.88621    
stateindiana          -6.220e+02  1.726e+03  -0.360  0.71861    
stateiowa             -2.294e+03  1.729e+03  -1.327  0.18477    
statekansas           -8.837e+02  1.721e+03  -0.514  0.60767    
statekentucky         -2.974e+02  1.688e+03  -0.176  0.86022    
statelouisiana        -3.582e+03  1.707e+03  -2.098  0.03607 *  
statemaine            -4.732e+02  1.735e+03  -0.273  0.78513    
statemaryland          6.694e+01  1.724e+03   0.039  0.96904    
statemassachusetts    -3.317e+02  1.722e+03  -0.193  0.84734    
statemichigan         -5.004e+03  1.741e+03  -2.874  0.00413 ** 
stateminnesota        -5.754e+03  1.767e+03  -3.256  0.00116 ** 
statemississippi      -2.389e+03  1.694e+03  -1.410  0.15872    
statemissouri         -1.393e+02  1.700e+03  -0.082  0.93473    
statemontana          -1.053e+04  1.761e+03  -5.979 2.92e-09 ***
statenebraska         -2.388e+03  1.741e+03  -1.372  0.17044    
statenew jersey       -1.159e+03  1.735e+03  -0.668  0.50429    
statenew mexico        5.369e+02  1.794e+03   0.299  0.76478    
statenew york         -2.291e+03  1.720e+03  -1.332  0.18298    
statenorth carolina   -7.721e+02  1.710e+03  -0.452  0.65160    
statenorth dakota     -2.866e+04  2.051e+03 -13.972  < 2e-16 ***
stateohio             -5.605e+02  1.703e+03  -0.329  0.74215    
stateoklahoma         -1.492e+03  1.722e+03  -0.867  0.38614    
stateoregon           -9.088e+03  1.768e+03  -5.142 3.15e-07 ***
stateother states     -3.600e+01  1.738e+03  -0.021  0.98348    
statepennsylvania     -7.084e+02  1.722e+03  -0.411  0.68083    
statesouth carolina   -6.225e+02  1.704e+03  -0.365  0.71500    
statesouth dakota     -9.922e+03  1.796e+03  -5.526 3.96e-08 ***
statetennessee         1.793e+02  1.686e+03   0.106  0.91531    
statetexas            -1.696e+04  1.897e+03  -8.943  < 2e-16 ***
stateutah             -1.383e+03  1.739e+03  -0.795  0.42665    
statevermont          -2.461e+02  1.737e+03  -0.142  0.88736    
statevirginia          2.207e+01  1.693e+03   0.013  0.98960    
statewashington       -7.111e+03  1.766e+03  -4.027 5.99e-05 ***
statewest virginia     5.712e+01  1.719e+03   0.033  0.97349    
statewisconsin        -3.376e+03  1.734e+03  -1.947  0.05173 .  
statewyoming          -1.104e+03  1.741e+03  -0.634  0.52627    
monthsQ2              -3.837e+03  5.025e+02  -7.635 4.40e-14 ***
monthsQ3              -7.368e+02  5.321e+02  -1.385  0.16645    
monthsQ4              -1.666e+03  5.087e+02  -3.274  0.00109 ** 
Varroa.mites           1.046e+03  1.326e+03   0.789  0.43052    
Other.pests.parasites -2.673e+03  2.045e+03  -1.307  0.19136    
Disesases             -1.091e+03  3.201e+03  -0.341  0.73331    
Pesticides             6.317e+03  2.546e+03   2.481  0.01323 *  
Other                  5.387e+03  3.218e+03   1.674  0.09433 .  
Unknown                8.291e+03  3.989e+03   2.078  0.03788 *  
year                  -2.192e+02  8.081e+01  -2.713  0.00676 ** 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 6398 on 1277 degrees of freedom
Multiple R-squared:  0.9296,    Adjusted R-squared:  0.9265 
F-statistic:   301 on 56 and 1277 DF,  p-value: < 2.2e-16
lin_mod <- lm(data=data, colony_lost_pct ~ state + months + Varroa.mites +Other.pests.parasites+Disesases+Pesticides+Other+Unknown)
summary(lin_mod)

Call:
lm(formula = colony_lost_pct ~ state + months + Varroa.mites + 
    Other.pests.parasites + Disesases + Pesticides + Other + 
    Unknown, data = data)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.15729 -0.03549 -0.00630  0.02579  0.52253 

Coefficients:
                       Estimate Std. Error t value Pr(>|t|)    
(Intercept)            0.134863   0.012040  11.201  < 2e-16 ***
statearizona           0.015616   0.015795   0.989 0.323023    
statearkansas         -0.014692   0.015738  -0.934 0.350698    
statecalifornia       -0.052587   0.015864  -3.315 0.000943 ***
statecolorado         -0.013548   0.016018  -0.846 0.397823    
stateconnecticut      -0.062775   0.015911  -3.945 8.40e-05 ***
stateflorida          -0.032538   0.015585  -2.088 0.037018 *  
stategeorgia          -0.027561   0.015677  -1.758 0.078988 .  
statehawaii           -0.073561   0.016600  -4.431 1.02e-05 ***
stateidaho            -0.055737   0.016010  -3.481 0.000516 ***
stateillinois         -0.004453   0.015628  -0.285 0.775714    
stateindiana          -0.014200   0.015805  -0.898 0.369130    
stateiowa             -0.046773   0.015817  -2.957 0.003162 ** 
statekansas            0.018607   0.015755   1.181 0.237832    
statekentucky         -0.015248   0.015462  -0.986 0.324255    
statelouisiana        -0.056640   0.015586  -3.634 0.000290 ***
statemaine            -0.042641   0.015890  -2.683 0.007380 ** 
statemaryland         -0.009554   0.015792  -0.605 0.545282    
statemassachusetts    -0.018497   0.015775  -1.173 0.241197    
statemichigan         -0.042525   0.015807  -2.690 0.007231 ** 
stateminnesota        -0.042932   0.015956  -2.691 0.007226 ** 
statemississippi      -0.039995   0.015486  -2.583 0.009916 ** 
statemissouri         -0.024174   0.015572  -1.552 0.120818    
statemontana          -0.085721   0.015855  -5.407 7.66e-08 ***
statenebraska         -0.040909   0.015914  -2.571 0.010261 *  
statenew jersey       -0.075657   0.015888  -4.762 2.13e-06 ***
statenew mexico        0.028963   0.016430   1.763 0.078172 .  
statenew york         -0.036030   0.015708  -2.294 0.021966 *  
statenorth carolina   -0.024098   0.015652  -1.540 0.123911    
statenorth dakota     -0.070309   0.015853  -4.435 1.00e-05 ***
stateohio             -0.017524   0.015596  -1.124 0.261389    
stateoklahoma         -0.039908   0.015759  -2.532 0.011448 *  
stateoregon           -0.077638   0.015956  -4.866 1.28e-06 ***
stateother states     -0.023476   0.015918  -1.475 0.140495    
statepennsylvania     -0.020514   0.015764  -1.301 0.193368    
statesouth carolina   -0.032838   0.015607  -2.104 0.035568 *  
statesouth dakota     -0.071388   0.015898  -4.490 7.75e-06 ***
statetennessee         0.008326   0.015440   0.539 0.589792    
statetexas            -0.044291   0.015597  -2.840 0.004588 ** 
stateutah             -0.031895   0.015919  -2.004 0.045326 *  
statevermont          -0.075638   0.015912  -4.754 2.22e-06 ***
statevirginia         -0.017684   0.015503  -1.141 0.254234    
statewashington       -0.052592   0.015967  -3.294 0.001015 ** 
statewest virginia    -0.023356   0.015739  -1.484 0.138071    
statewisconsin        -0.045103   0.015824  -2.850 0.004437 ** 
statewyoming          -0.038614   0.015935  -2.423 0.015521 *  
monthsQ2              -0.060056   0.004596 -13.066  < 2e-16 ***
monthsQ3              -0.038871   0.004859  -8.000 2.76e-15 ***
monthsQ4              -0.027263   0.004640  -5.876 5.37e-09 ***
Varroa.mites           0.076841   0.012092   6.355 2.90e-10 ***
Other.pests.parasites -0.050901   0.018723  -2.719 0.006644 ** 
Disesases              0.026032   0.029249   0.890 0.373626    
Pesticides             0.009709   0.023218   0.418 0.675903    
Other                  0.264096   0.029433   8.973  < 2e-16 ***
Unknown                0.179917   0.036496   4.930 9.31e-07 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.05859 on 1279 degrees of freedom
Multiple R-squared:  0.3859,    Adjusted R-squared:   0.36 
F-statistic: 14.88 on 54 and 1279 DF,  p-value: < 2.2e-16
library(car)
Loading required package: carData

Attaching package: ‘car’

The following object is masked from ‘package:dplyr’:

    recode
b <- coefficients(lin_mod)
e <- residuals(lin_mod)

cat("Verify the hypothesis:\n")
Verify the hypothesis:
par(mfrow=c(2,2))
plot(lin_mod)


par(mfrow=c(1,1))

cat("Verify normality of residuals:\n")
Verify normality of residuals:
shapiro.test(residuals(lin_mod))

    Shapiro-Wilk normality test

data:  residuals(lin_mod)
W = 0.92142, p-value < 2.2e-16
shapiro.test(rstudent(lin_mod))

    Shapiro-Wilk normality test

data:  rstudent(lin_mod)
W = 0.91839, p-value < 2.2e-16
cat("VIF:\n")
VIF:
vif(lin_mod)
                          GVIF Df GVIF^(1/(2*Df))
state                 3.833007 45        1.015041
months                1.223296  3        1.034162
Varroa.mites          2.070817  1        1.439033
Other.pests.parasites 2.466830  1        1.570615
Disesases             1.399190  1        1.182874
Pesticides            1.684843  1        1.298015
Other                 1.381107  1        1.175205
Unknown               1.301936  1        1.141024

Le ipotesi del modello lineare non sono verificate.

LOGIT

Non so se logit va bene visto che abbiamo valori nell’intervallo 0-1 e non 0,1.

data = data %>% mutate(logit_colony_lost_pct=logit(colony_lost_pct))
Warning: proportions remapped to (0.025, 0.975)
logit_mod <- lm(data=data, logit_colony_lost_pct ~ state + months + Varroa.mites +Other.pests.parasites+Disesases+Pesticides+Other+Unknown)
summary(logit_mod)

Call:
lm(formula = logit_colony_lost_pct ~ state + months + Varroa.mites + 
    Other.pests.parasites + Disesases + Pesticides + Other + 
    Unknown, data = data)

Residuals:
     Min       1Q   Median       3Q      Max 
-1.50339 -0.28129 -0.00443  0.28040  2.52331 

Coefficients:
                       Estimate Std. Error t value Pr(>|t|)    
(Intercept)           -1.863163   0.096789 -19.250  < 2e-16 ***
statearizona           0.125178   0.126981   0.986 0.324415    
statearkansas         -0.116832   0.126518  -0.923 0.355950    
statecalifornia       -0.336849   0.127533  -2.641 0.008360 ** 
statecolorado         -0.111448   0.128768  -0.865 0.386929    
stateconnecticut      -0.565718   0.127910  -4.423 1.06e-05 ***
stateflorida          -0.183202   0.125293  -1.462 0.143936    
stategeorgia          -0.140358   0.126033  -1.114 0.265635    
statehawaii           -0.828533   0.133449  -6.209 7.21e-10 ***
stateidaho            -0.391134   0.128707  -3.039 0.002422 ** 
stateillinois         -0.019218   0.125636  -0.153 0.878452    
stateindiana          -0.093504   0.127058  -0.736 0.461917    
stateiowa             -0.315402   0.127153  -2.480 0.013248 *  
statekansas            0.080232   0.126660   0.633 0.526559    
statekentucky         -0.107016   0.124302  -0.861 0.389435    
statelouisiana        -0.479374   0.125298  -3.826 0.000137 ***
statemaine            -0.374422   0.127743  -2.931 0.003438 ** 
statemaryland         -0.121152   0.126955  -0.954 0.340118    
statemassachusetts    -0.227338   0.126816  -1.793 0.073264 .  
statemichigan         -0.328098   0.127071  -2.582 0.009933 ** 
stateminnesota        -0.333974   0.128276  -2.604 0.009333 ** 
statemississippi      -0.273962   0.124497  -2.201 0.027946 *  
statemissouri         -0.214895   0.125187  -1.717 0.086297 .  
statemontana          -0.845197   0.127459  -6.631 4.90e-11 ***
statenebraska         -0.309949   0.127931  -2.423 0.015540 *  
statenew jersey       -0.763339   0.127722  -5.977 2.95e-09 ***
statenew mexico        0.007216   0.132083   0.055 0.956441    
statenew york         -0.260273   0.126277  -2.061 0.039493 *  
statenorth carolina   -0.142962   0.125829  -1.136 0.256101    
statenorth dakota     -0.664777   0.127447  -5.216 2.13e-07 ***
stateohio             -0.162257   0.125377  -1.294 0.195847    
stateoklahoma         -0.420574   0.126690  -3.320 0.000927 ***
stateoregon           -0.623852   0.128276  -4.863 1.30e-06 ***
stateother states     -0.191665   0.127963  -1.498 0.134427    
statepennsylvania     -0.175791   0.126727  -1.387 0.165632    
statesouth carolina   -0.190429   0.125468  -1.518 0.129324    
statesouth dakota     -0.608582   0.127808  -4.762 2.14e-06 ***
statetennessee         0.056411   0.124122   0.454 0.649561    
statetexas            -0.290287   0.125390  -2.315 0.020767 *  
stateutah             -0.191698   0.127974  -1.498 0.134393    
statevermont          -0.809742   0.127916  -6.330 3.38e-10 ***
statevirginia         -0.108980   0.124633  -0.874 0.382061    
statewashington       -0.411207   0.128359  -3.204 0.001391 ** 
statewest virginia    -0.179734   0.126531  -1.420 0.155713    
statewisconsin        -0.335018   0.127207  -2.634 0.008549 ** 
statewyoming          -0.301592   0.128103  -2.354 0.018709 *  
monthsQ2              -0.480356   0.036952 -13.000  < 2e-16 ***
monthsQ3              -0.252232   0.039059  -6.458 1.51e-10 ***
monthsQ4              -0.160444   0.037302  -4.301 1.83e-05 ***
Varroa.mites           0.664529   0.097210   6.836 1.26e-11 ***
Other.pests.parasites -0.333413   0.150519  -2.215 0.026930 *  
Disesases              0.269497   0.235134   1.146 0.251951    
Pesticides             0.038898   0.186651   0.208 0.834949    
Other                  1.956228   0.236612   8.268 3.39e-16 ***
Unknown                1.540075   0.293393   5.249 1.79e-07 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.471 on 1279 degrees of freedom
Multiple R-squared:  0.4206,    Adjusted R-squared:  0.3961 
F-statistic: 17.19 on 54 and 1279 DF,  p-value: < 2.2e-16
AIC(logit_mod)
[1] 1833.06
cat("Verify the hypothesis:\n")
Verify the hypothesis:
par(mfrow=c(2,2))
plot(logit_mod)


par(mfrow=c(1,1))

cat("Verify normality of residuals:\n")
Verify normality of residuals:
shapiro.test(residuals(logit_mod))

    Shapiro-Wilk normality test

data:  residuals(logit_mod)
W = 0.99192, p-value = 1.087e-06
shapiro.test(rstudent(logit_mod))

    Shapiro-Wilk normality test

data:  rstudent(logit_mod)
W = 0.99162, p-value = 6.91e-07
cat("VIF:\n")
VIF:
vif(logit_mod)
                          GVIF Df GVIF^(1/(2*Df))
state                 3.833007 45        1.015041
months                1.223296  3        1.034162
Varroa.mites          2.070817  1        1.439033
Other.pests.parasites 2.466830  1        1.570615
Disesases             1.399190  1        1.182874
Pesticides            1.684843  1        1.298015
Other                 1.381107  1        1.175205
Unknown               1.301936  1        1.141024
library(outliers)
x = outlierTest(logit_mod)
x
data_without_outliers = data[-c(897,921),]

logit_mod <- lm(data=data_without_outliers, logit_colony_lost_pct ~ state + months + Varroa.mites +Other.pests.parasites+Disesases+Pesticides+Other+Unknown)
summary(logit_mod)

Call:
lm(formula = logit_colony_lost_pct ~ state + months + Varroa.mites + 
    Other.pests.parasites + Disesases + Pesticides + Other + 
    Unknown, data = data_without_outliers)

Residuals:
     Min       1Q   Median       3Q      Max 
-1.49916 -0.27711 -0.00105  0.27992  1.48858 

Coefficients:
                      Estimate Std. Error t value Pr(>|t|)    
(Intercept)           -1.93736    0.09651 -20.075  < 2e-16 ***
statearizona           0.19470    0.12592   1.546 0.122309    
statearkansas         -0.04715    0.12546  -0.376 0.707100    
statecalifornia       -0.26709    0.12645  -2.112 0.034867 *  
statecolorado         -0.04120    0.12766  -0.323 0.746956    
stateconnecticut      -0.49594    0.12681  -3.911 9.69e-05 ***
stateflorida          -0.11452    0.12428  -0.921 0.356997    
stategeorgia          -0.07181    0.12498  -0.575 0.565674    
statehawaii           -0.77134    0.13198  -5.844 6.45e-09 ***
stateidaho            -0.32082    0.12759  -2.514 0.012046 *  
stateillinois          0.04972    0.12461   0.399 0.689990    
stateindiana          -0.02313    0.12599  -0.184 0.854342    
stateiowa             -0.24572    0.12608  -1.949 0.051524 .  
statekansas            0.14937    0.12561   1.189 0.234603    
statekentucky         -0.04021    0.12328  -0.326 0.744348    
statelouisiana        -0.41179    0.12422  -3.315 0.000942 ***
statemaine            -0.30409    0.12666  -2.401 0.016498 *  
statemaryland         -0.05177    0.12589  -0.411 0.680979    
statemassachusetts    -0.15715    0.12575  -1.250 0.211646    
statemichigan         -0.25831    0.12600  -2.050 0.040554 *  
stateminnesota        -0.26209    0.12721  -2.060 0.039570 *  
statemississippi      -0.20658    0.12346  -1.673 0.094523 .  
statemissouri         -0.23694    0.12518  -1.893 0.058601 .  
statemontana          -0.77537    0.12638  -6.135 1.13e-09 ***
statenebraska         -0.23915    0.12684  -1.885 0.059606 .  
statenew jersey       -0.69306    0.12663  -5.473 5.32e-08 ***
statenew mexico        0.07706    0.13085   0.589 0.556013    
statenew york         -0.19113    0.12523  -1.526 0.127193    
statenorth carolina   -0.07455    0.12478  -0.597 0.550317    
statenorth dakota     -0.59503    0.12636  -4.709 2.76e-06 ***
stateohio             -0.09427    0.12434  -0.758 0.448504    
stateoklahoma         -0.35096    0.12563  -2.794 0.005289 ** 
stateoregon           -0.55400    0.12716  -4.357 1.43e-05 ***
stateother states     -0.12142    0.12687  -0.957 0.338727    
statepennsylvania     -0.10636    0.12566  -0.846 0.397481    
statesouth carolina   -0.12252    0.12440  -0.985 0.324849    
statesouth dakota     -0.53986    0.12671  -4.261 2.19e-05 ***
statetennessee         0.12237    0.12307   0.994 0.320264    
statetexas            -0.22139    0.12434  -1.780 0.075240 .  
stateutah             -0.12091    0.12689  -0.953 0.340838    
statevermont          -0.73923    0.12681  -5.829 7.04e-09 ***
statevirginia         -0.04197    0.12359  -0.340 0.734230    
statewashington       -0.34118    0.12725  -2.681 0.007429 ** 
statewest virginia    -0.11115    0.12546  -0.886 0.375806    
statewisconsin        -0.26449    0.12618  -2.096 0.036258 *  
statewyoming          -0.23105    0.12701  -1.819 0.069120 .  
monthsQ2              -0.47955    0.03638 -13.183  < 2e-16 ***
monthsQ3              -0.24593    0.03841  -6.403 2.14e-10 ***
monthsQ4              -0.15358    0.03669  -4.186 3.03e-05 ***
Varroa.mites           0.66679    0.09554   6.979 4.77e-12 ***
Other.pests.parasites -0.30955    0.14799  -2.092 0.036657 *  
Disesases              0.25958    0.23110   1.123 0.261561    
Pesticides             0.01682    0.18348   0.092 0.926982    
Other                  1.96691    0.23257   8.457  < 2e-16 ***
Unknown                1.52945    0.28844   5.303 1.34e-07 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.463 on 1277 degrees of freedom
Multiple R-squared:  0.4289,    Adjusted R-squared:  0.4047 
F-statistic: 17.76 on 54 and 1277 DF,  p-value: < 2.2e-16
AIC(logit_mod)
[1] 1784.272
cat("Verify the hypothesis:\n")
Verify the hypothesis:
par(mfrow=c(2,2))
plot(logit_mod)


par(mfrow=c(1,1))

cat("Verify normality of residuals:\n")
Verify normality of residuals:
shapiro.test(residuals(logit_mod))

    Shapiro-Wilk normality test

data:  residuals(logit_mod)
W = 0.99589, p-value = 0.001175
shapiro.test(rstudent(logit_mod))

    Shapiro-Wilk normality test

data:  rstudent(logit_mod)
W = 0.99573, p-value = 0.0008545
cat("VIF:\n")
VIF:
vif(logit_mod)
                          GVIF Df GVIF^(1/(2*Df))
state                 3.831742 45        1.015038
months                1.223416  3        1.034179
Varroa.mites          2.068878  1        1.438359
Other.pests.parasites 2.467406  1        1.570798
Disesases             1.399037  1        1.182809
Pesticides            1.685009  1        1.298079
Other                 1.380845  1        1.175094
Unknown               1.301451  1        1.140811
# GLM NON DA USARE
logit_mod <- glm(colony_lost_pct ~ months + state + Varroa.mites +Other.pests.parasites+Disesases+Pesticides+Other+Unknown,
                  data = data,family = "binomial")
Warning: non-integer #successes in a binomial glm!
summary(logit_mod)

Call:
glm(formula = colony_lost_pct ~ months + state + Varroa.mites + 
    Other.pests.parasites + Disesases + Pesticides + Other + 
    Unknown, family = "binomial", data = data)

Deviance Residuals: 
     Min        1Q    Median        3Q       Max  
-0.51622  -0.12254  -0.02614   0.08359   1.23458  

Coefficients:
                      Estimate Std. Error z value Pr(>|z|)   
(Intercept)           -1.87893    0.58832  -3.194   0.0014 **
monthsQ2              -0.62693    0.26177  -2.395   0.0166 * 
monthsQ3              -0.36568    0.26049  -1.404   0.1604   
monthsQ4              -0.25561    0.24458  -1.045   0.2960   
statearizona           0.10685    0.74269   0.144   0.8856   
statearkansas         -0.13023    0.76868  -0.169   0.8655   
statecalifornia       -0.44946    0.81323  -0.553   0.5805   
statecolorado         -0.10110    0.78789  -0.128   0.8979   
stateconnecticut      -0.71172    0.92716  -0.768   0.4427   
stateflorida          -0.26476    0.76885  -0.344   0.7306   
stategeorgia          -0.23230    0.76944  -0.302   0.7627   
statehawaii           -1.01425    1.05688  -0.960   0.3372   
stateidaho            -0.50608    0.84083  -0.602   0.5473   
stateillinois         -0.03364    0.76400  -0.044   0.9649   
stateindiana          -0.12667    0.78542  -0.161   0.8719   
stateiowa             -0.44666    0.82159  -0.544   0.5867   
statekansas            0.05247    0.73055   0.072   0.9427   
statekentucky         -0.13283    0.75587  -0.176   0.8605   
statelouisiana        -0.61109    0.87970  -0.695   0.4873   
statemaine            -0.42119    0.85611  -0.492   0.6227   
statemaryland         -0.08836    0.79405  -0.111   0.9114   
statemassachusetts    -0.16292    0.80531  -0.202   0.8397   
statemichigan         -0.38803    0.82144  -0.472   0.6367   
stateminnesota        -0.38615    0.84246  -0.458   0.6467   
statemississippi      -0.37148    0.80912  -0.459   0.6462   
statemissouri         -0.23806    0.79868  -0.298   0.7657   
statemontana          -1.01201    0.96980  -1.044   0.2967   
statenebraska         -0.39720    0.86743  -0.458   0.6470   
statenew jersey       -0.99334    1.01737  -0.976   0.3289   
statenew mexico        0.17811    0.78695   0.226   0.8209   
statenew york         -0.31611    0.80581  -0.392   0.6948   
statenorth carolina   -0.20728    0.77961  -0.266   0.7903   
statenorth dakota     -0.76106    0.92172  -0.826   0.4090   
stateohio             -0.14481    0.75984  -0.191   0.8489   
stateoklahoma         -0.38133    0.84739  -0.450   0.6527   
stateoregon           -0.79084    0.90686  -0.872   0.3832   
stateother states     -0.20610    0.82371  -0.250   0.8024   
statepennsylvania     -0.17917    0.79871  -0.224   0.8225   
statesouth carolina   -0.29410    0.80306  -0.366   0.7142   
statesouth dakota     -0.75117    0.89573  -0.839   0.4017   
statetennessee         0.05660    0.73788   0.077   0.9389   
statetexas            -0.41221    0.83373  -0.494   0.6210   
stateutah             -0.28115    0.81209  -0.346   0.7292   
statevermont          -1.00318    1.02503  -0.979   0.3277   
statevirginia         -0.14226    0.77335  -0.184   0.8541   
statewashington       -0.50922    0.87180  -0.584   0.5592   
statewest virginia    -0.20013    0.80116  -0.250   0.8027   
statewisconsin        -0.39115    0.79841  -0.490   0.6242   
statewyoming          -0.36901    0.85976  -0.429   0.6678   
Varroa.mites           0.73697    0.62098   1.187   0.2353   
Other.pests.parasites -0.39809    0.98457  -0.404   0.6860   
Disesases              0.14682    1.37740   0.107   0.9151   
Pesticides             0.07104    1.17181   0.061   0.9517   
Other                  2.25375    1.43033   1.576   0.1151   
Unknown                1.52043    1.74241   0.873   0.3829   
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 67.769  on 1333  degrees of freedom
Residual deviance: 40.343  on 1279  degrees of freedom
AIC: 437.26

Number of Fisher Scoring iterations: 5
AIC(logit_mod)
[1] 437.2587
cat("Verify the hypothesis:\n")
Verify the hypothesis:
par(mfrow=c(2,2))
plot(logit_mod)


par(mfrow=c(1,1))

cat("Verify normality of residuals:\n")
Verify normality of residuals:
shapiro.test(residuals(logit_mod))

    Shapiro-Wilk normality test

data:  residuals(logit_mod)
W = 0.97137, p-value = 1.322e-15
shapiro.test(rstudent(logit_mod))

    Shapiro-Wilk normality test

data:  rstudent(logit_mod)
W = 0.97006, p-value = 5.355e-16
cat("VIF:\n")
VIF:
vif(logit_mod)
                          GVIF Df GVIF^(1/(2*Df))
months                1.268615  3        1.040451
state                 3.524591 45        1.014096
Varroa.mites          1.950512  1        1.396607
Other.pests.parasites 2.144513  1        1.464416
Disesases             1.450458  1        1.204349
Pesticides            1.718088  1        1.310758
Other                 1.443224  1        1.201343
Unknown               1.297506  1        1.139081

BETA REGRESSION

require(betareg)
beta_mod <- betareg(colony_lost_pct ~ months + Varroa.mites + Other.pests.parasites+Disesases+Pesticides+Other+Unknown + state,
                  data = data)
summary(beta_mod)
AIC(beta_mod)

Linear Mixed Models

library(lme4)
lm_mod <- lmer(colony_lost_pct ~ year + months + Varroa.mites +Other.pests.parasites+Disesases+Pesticides+Other+Unknown + (1|state),
                  data = data)
summary(lm_mod)
Linear mixed model fit by REML ['lmerMod']
Formula: colony_lost_pct ~ year + months + Varroa.mites + Other.pests.parasites +  
    Disesases + Pesticides + Other + Unknown + (1 | state)
   Data: data

REML criterion at convergence: -3638.7

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-2.6402 -0.5915 -0.1267  0.4281  9.0569 

Random effects:
 Groups   Name        Variance  Std.Dev.
 state    (Intercept) 0.0005931 0.02435 
 Residual             0.0034048 0.05835 
Number of obs: 1334, groups:  state, 46

Fixed effects:
                        Estimate Std. Error t value
(Intercept)            5.1556871  1.4868102   3.468
year                  -0.0025048  0.0007366  -3.401
monthsQ2              -0.0601780  0.0045730 -13.159
monthsQ3              -0.0403626  0.0048315  -8.354
monthsQ4              -0.0287235  0.0046271  -6.208
Varroa.mites           0.0816173  0.0119049   6.856
Other.pests.parasites -0.0504874  0.0176579  -2.859
Disesases              0.0175948  0.0287917   0.611
Pesticides             0.0037462  0.0227962   0.164
Other                  0.2627312  0.0290583   9.042
Unknown                0.1925000  0.0358441   5.370

Correlation of Fixed Effects:
            (Intr) year   mnthQ2 mnthQ3 mnthQ4 Vrr.mt Othr.. Dissss Pstcds Other 
year        -1.000                                                               
monthsQ2    -0.010  0.008                                                        
monthsQ3    -0.072  0.071  0.500                                                 
monthsQ4    -0.080  0.079  0.484  0.511                                          
Varroa.mits  0.058 -0.059 -0.117 -0.230 -0.170                                   
Othr.psts.p  0.017 -0.017 -0.019 -0.061 -0.025 -0.386                            
Disesases   -0.063  0.063 -0.005  0.043 -0.008 -0.097 -0.126                     
Pesticides  -0.086  0.086 -0.082 -0.144 -0.083 -0.174 -0.154 -0.174              
Other       -0.047  0.047 -0.009  0.046  0.123 -0.144 -0.046 -0.151 -0.128       
Unknown     -0.045  0.044  0.127  0.095  0.020 -0.050 -0.055 -0.011 -0.057 -0.129
AIC(lm_mod)
[1] -3612.748
lm_mod <- lmer(colony_lost_pct ~ year + months + Varroa.mites +Other.pests.parasites+Disesases+Pesticides+Other+Unknown + (1|state),
                  data = data)
summary(lm_mod)
Linear mixed model fit by REML ['lmerMod']
Formula: colony_lost_pct ~ year + months + Varroa.mites + Other.pests.parasites +  
    Disesases + Pesticides + Other + Unknown + (1 | state)
   Data: data

REML criterion at convergence: -3638.7

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-2.6402 -0.5915 -0.1267  0.4281  9.0569 

Random effects:
 Groups   Name        Variance  Std.Dev.
 state    (Intercept) 0.0005931 0.02435 
 Residual             0.0034048 0.05835 
Number of obs: 1334, groups:  state, 46

Fixed effects:
                        Estimate Std. Error t value
(Intercept)            5.1556871  1.4868102   3.468
year                  -0.0025048  0.0007366  -3.401
monthsQ2              -0.0601780  0.0045730 -13.159
monthsQ3              -0.0403626  0.0048315  -8.354
monthsQ4              -0.0287235  0.0046271  -6.208
Varroa.mites           0.0816173  0.0119049   6.856
Other.pests.parasites -0.0504874  0.0176579  -2.859
Disesases              0.0175948  0.0287917   0.611
Pesticides             0.0037462  0.0227962   0.164
Other                  0.2627312  0.0290583   9.042
Unknown                0.1925000  0.0358441   5.370

Correlation of Fixed Effects:
            (Intr) year   mnthQ2 mnthQ3 mnthQ4 Vrr.mt Othr.. Dissss Pstcds Other 
year        -1.000                                                               
monthsQ2    -0.010  0.008                                                        
monthsQ3    -0.072  0.071  0.500                                                 
monthsQ4    -0.080  0.079  0.484  0.511                                          
Varroa.mits  0.058 -0.059 -0.117 -0.230 -0.170                                   
Othr.psts.p  0.017 -0.017 -0.019 -0.061 -0.025 -0.386                            
Disesases   -0.063  0.063 -0.005  0.043 -0.008 -0.097 -0.126                     
Pesticides  -0.086  0.086 -0.082 -0.144 -0.083 -0.174 -0.154 -0.174              
Other       -0.047  0.047 -0.009  0.046  0.123 -0.144 -0.046 -0.151 -0.128       
Unknown     -0.045  0.044  0.127  0.095  0.020 -0.050 -0.055 -0.011 -0.057 -0.129
AIC(lm_mod)
[1] -3612.748
fm16.1mer = lm_mod
plot(fm16.1mer)

shapiro.test(residuals(fm16.1mer))

    Shapiro-Wilk normality test

data:  residuals(fm16.1mer)
W = 0.9154, p-value < 2.2e-16
library(lme4)
library(insight)
confint(fm16.1mer,oldNames=TRUE)
Computing profile confidence intervals ...
                            2.5 %      97.5 %
.sig01                 0.01867574  0.03083460
.sigma                 0.05621247  0.06072823
(Intercept)            0.08897113  0.10997659
monthsQ2              -0.06902405 -0.05107161
monthsQ3              -0.04866316 -0.02974364
monthsQ4              -0.03654416 -0.01843508
Varroa.mites           0.05598346  0.10266234
Other.pests.parasites -0.08610262 -0.01690467
Disesases             -0.03265312  0.08011542
Pesticides            -0.03410858  0.05500108
Other                  0.21048896  0.32443905
Unknown                0.12782586  0.26913349
## Var-Cov matrix of fixed-effects
vcovb <- vcov(fm16.1mer) 
cat("\nVar-Cov matrix of fixed-effects:\n")

Var-Cov matrix of fixed-effects:
vcovb
10 x 10 Matrix of class "dpoMatrix"
                        (Intercept)      monthsQ2      monthsQ3      monthsQ4  Varroa.mites
(Intercept)            2.878523e-05 -8.383407e-06 -6.776304e-06 -7.886569e-06 -1.901355e-05
monthsQ2              -8.383407e-06  2.108707e-05  1.112091e-05  1.031227e-05 -6.413347e-06
monthsQ3              -6.776304e-06  1.112091e-05  2.341912e-05  1.138887e-05 -1.311044e-05
monthsQ4              -7.886569e-06  1.031227e-05  1.138887e-05  2.145541e-05 -9.192287e-06
Varroa.mites          -1.901355e-05 -6.413347e-06 -1.311044e-05 -9.192287e-06  1.423791e-04
Other.pests.parasites  8.964961e-07 -1.523843e-06 -5.156934e-06 -1.972464e-06 -8.200498e-05
Disesases              3.652104e-06 -7.575724e-07  5.395792e-06 -1.793143e-06 -3.223109e-05
Pesticides             8.796375e-06 -8.649383e-06 -1.668943e-05 -9.601333e-06 -4.618682e-05
Other                 -2.327472e-05 -1.306918e-06  6.021490e-06  1.614666e-05 -4.923656e-05
Unknown               -3.917203e-05  2.087241e-05  1.609280e-05  2.723386e-06 -2.059026e-05
                      Other.pests.parasites     Disesases    Pesticides         Other
(Intercept)                    8.964961e-07  3.652104e-06  8.796375e-06 -2.327472e-05
monthsQ2                      -1.523843e-06 -7.575724e-07 -8.649383e-06 -1.306918e-06
monthsQ3                      -5.156934e-06  5.395792e-06 -1.668943e-05  6.021490e-06
monthsQ4                      -1.972464e-06 -1.793143e-06 -9.601333e-06  1.614666e-05
Varroa.mites                  -8.200498e-05 -3.223109e-05 -4.618682e-05 -4.923656e-05
Other.pests.parasites          3.138972e-04 -6.395886e-05 -6.182230e-05 -2.336295e-05
Disesases                     -6.395886e-05  8.323018e-04 -1.189189e-04 -1.302263e-04
Pesticides                    -6.182230e-05 -1.189189e-04  5.199147e-04 -8.791086e-05
Other                         -2.336295e-05 -1.302263e-04 -8.791086e-05  8.494389e-04
Unknown                       -3.462251e-05 -1.426727e-05 -5.012196e-05 -1.373550e-04
                            Unknown
(Intercept)           -3.917203e-05
monthsQ2               2.087241e-05
monthsQ3               1.609280e-05
monthsQ4               2.723386e-06
Varroa.mites          -2.059026e-05
Other.pests.parasites -3.462251e-05
Disesases             -1.426727e-05
Pesticides            -5.012196e-05
Other                 -1.373550e-04
Unknown                1.292646e-03
corb <- cov2cor(vcovb) 
nms <- abbreviate(names(fixef(fm16.1mer)), 5)
rownames(corb) <- nms
cat("\nCorrelation matrix of fixed-effects:\n")

Correlation matrix of fixed-effects:
corb
10 x 10 Matrix of class "dpoMatrix"
                       (Intercept)     monthsQ2    monthsQ3    monthsQ4 Varroa.mites
(Intercept)            1.000000000 -0.340273055 -0.26098937 -0.31734737  -0.29699917
monthsQ2              -0.340273055  1.000000000  0.50043425  0.48481701  -0.11704517
monthsQ3              -0.260989373  0.500434247  1.00000000  0.50807389  -0.22704349
monthsQ4              -0.317347372  0.484817007  0.50807389  1.00000000  -0.16631526
Varroa.mites          -0.296999172 -0.117045171 -0.22704349 -0.16631526   1.00000000
Other.pests.parasites  0.009431263 -0.018730025 -0.06014681 -0.02403515  -0.38790325
Disesases              0.023594889 -0.005718413  0.03864822 -0.01341857  -0.09362924
Pesticides             0.071903970 -0.082605876 -0.15124818 -0.09090695  -0.16975749
Other                 -0.148844779 -0.009765045  0.04269260  0.11960471  -0.14157890
Unknown               -0.203072614  0.126422543  0.09249247  0.01635313  -0.04799532
                      Other.pests.parasites    Disesases  Pesticides        Other     Unknown
(Intercept)                     0.009431263  0.023594889  0.07190397 -0.148844779 -0.20307261
monthsQ2                       -0.018730025 -0.005718413 -0.08260588 -0.009765045  0.12642254
monthsQ3                       -0.060146806  0.038648223 -0.15124818  0.042692602  0.09249247
monthsQ4                       -0.024035152 -0.013418566 -0.09090695  0.119604710  0.01635313
Varroa.mites                   -0.387903252 -0.093629240 -0.16975749 -0.141578903 -0.04799532
Other.pests.parasites           1.000000000 -0.125131469 -0.15303309 -0.045244719 -0.05435317
Disesases                      -0.125131469  1.000000000 -0.18077747 -0.154878868 -0.01375500
Pesticides                     -0.153033095 -0.180777468  1.00000000 -0.132284935 -0.06113953
Other                          -0.045244719 -0.154878868 -0.13228493  1.000000000 -0.13108059
Unknown                        -0.054353173 -0.013755004 -0.06113953 -0.131080587  1.00000000
cat("Var-Cov matrix of random-effects and errors\n")
Var-Cov matrix of random-effects and errors
print(vc <- VarCorr(fm16.1mer), comp = c("Variance", "Std.Dev."))
 Groups   Name        Variance   Std.Dev.
 state    (Intercept) 0.00058802 0.024249
 Residual             0.00343356 0.058597
sigma2_eps <- as.numeric(get_variance_residual(fm16.1mer))
cat("the variance associated to eps sigma2_eps is",sigma2_eps)
the variance associated to eps sigma2_eps is 0.003433556
sigma2_b <- as.numeric(get_variance_random(fm16.1mer))
cat("the variance associated to random effect sigma2_b is",sigma2_b)
the variance associated to random effect sigma2_b is 0.0005880246
## Let's compute the conditional and marginal var-cov matrix of Y
sgma <- summary(fm16.1mer)$sigma  # sigma^2

A <- getME(fm16.1mer, "A") # A  --> N x n, A represents the D (not italic), variance of random effect
I.n <- Diagonal(ncol(A)) # IN  --> n x n

## the conditional variance-covariance matrix of Y (diagonal matrix)
## conditional to the random effect è semplicemente la matrice fixed effect
cat("\n SigmaErr:\n")

 SigmaErr:
SigmaErr = sgma^2 * (I.n)
# SigmaErr ha dimensione n_oss x n_oss

# Conditioned to the random effects b_i, we observe the var-cov of the errors
# that are independent and homoscedastic

## we visualize the first 20 rows/columns of the matrix
plot(as.matrix(SigmaErr[1:20,1:20]), main = 'Conditional estimated Var-Cov matrix of Y')


cat("the MARGINAL variance-covariance matrix of Y (block-diagonal matrix) is")
the MARGINAL variance-covariance matrix of Y (block-diagonal matrix) is
V <- sgma^2 * (I.n + crossprod(A)) # V = s^2*(I_N+A*A) --> s^2*(I_N) is the error part, s^2*(A*A) is the random effect part
  #-> V is a block-diagional matrix, the marginal var-cov matrix

# visualization of the first 20 rows/columns
plot(as.matrix(V[1:20,1:20]), main = 'Marginal estimated Var-Cov matrix of Y')



# Another way to interpret the variance output is to note percentage of the subject variance out 
# of the total, i.e. the Percentage of Variance explained by the Random Effect (PVRE).
# This is also called the intraclass correlation (ICC), because it is also an estimate of the within 
# cluster correlation.

PVRE <- sigma2_b/(sigma2_b+sigma2_eps)
cat("The Proportion of Variance due to Random Effect is",PVRE) # 15% is quite high! 
The Proportion of Variance due to Random Effect is 0.1462173
cat("\nvisualization of the random intercepts with their 95% confidence intervals in the dotplot\n")

visualization of the random intercepts with their 95% confidence intervals in the dotplot
# Random effects: b_0i for i=1,...,234
dotplot(ranef(fm16.1mer, condVar=T))
$state

library(plotly)
x = ranef(fm16.1mer, condVar=T)
us_data <- map_data("state")
df <- data.frame(
  state = tolower(rownames(x$state)),
  values = x$state$`(Intercept)`
)
library(usmap)
plot_usmap(data = df) + labs(title = "Cluster by prec")

# 1) Assessing Assumption on the within-group errors
#it's just a sample from the entire population, so to take with care

plot(fm16.1mer)  ## Pearson and raw residuals are the same now


qqnorm(resid(fm16.1mer))
qqline(resid(fm16.1mer), col='red', lwd=2)

shapiro.test(resid(fm16.1mer))

    Shapiro-Wilk normality test

data:  resid(fm16.1mer)
W = 0.9154, p-value < 2.2e-16
# 2) Assessing Assumption on the Random Effects

qqnorm(unlist(ranef(fm16.1mer)$state), main='Normal Q-Q Plot - Random Effects on Intercept')
qqline(unlist(ranef(fm16.1mer)$state), col='red', lwd=2)

shapiro.test(unlist(ranef(fm16.1mer)$state))

    Shapiro-Wilk normality test

data:  unlist(ranef(fm16.1mer)$state)
W = 0.98279, p-value = 0.7216
AIC(fm16.1mer)
[1] -3615.818
lm_mod_log <- lmer(logit_colony_lost_pct ~ year + months + Varroa.mites +Other.pests.parasites+Disesases+Pesticides+Other+Unknown + (1|state),
                  data = data)
summary(lm_mod_log)
Linear mixed model fit by REML ['lmerMod']
Formula: 
logit_colony_lost_pct ~ year + months + Varroa.mites + Other.pests.parasites +  
    Disesases + Pesticides + Other + Unknown + (1 | state)
   Data: data

REML criterion at convergence: 1880.8

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-3.1235 -0.5770 -0.0122  0.5902  5.5002 

Random effects:
 Groups   Name        Variance Std.Dev.
 state    (Intercept) 0.05026  0.2242  
 Residual             0.21903  0.4680  
Number of obs: 1334, groups:  state, 46

Fixed effects:
                       Estimate Std. Error t value
(Intercept)           47.653452  11.926652   3.996
year                  -0.024679   0.005908  -4.177
monthsQ2              -0.481306   0.036686 -13.120
monthsQ3              -0.265882   0.038783  -6.856
monthsQ4              -0.173906   0.037125  -4.684
Varroa.mites           0.703712   0.095744   7.350
Other.pests.parasites -0.345946   0.143167  -2.416
Disesases              0.180222   0.231564   0.778
Pesticides             0.001939   0.183514   0.011
Other                  1.956701   0.233538   8.379
Unknown                1.647476   0.288376   5.713

Correlation of Fixed Effects:
            (Intr) year   mnthQ2 mnthQ3 mnthQ4 Vrr.mt Othr.. Dissss Pstcds Other 
year        -1.000                                                               
monthsQ2    -0.010  0.008                                                        
monthsQ3    -0.072  0.071  0.500                                                 
monthsQ4    -0.080  0.079  0.484  0.511                                          
Varroa.mits  0.058 -0.059 -0.118 -0.232 -0.171                                   
Othr.psts.p  0.018 -0.018 -0.020 -0.063 -0.027 -0.382                            
Disesases   -0.064  0.064 -0.005  0.043 -0.008 -0.095 -0.132                     
Pesticides  -0.087  0.087 -0.081 -0.144 -0.083 -0.173 -0.159 -0.172              
Other       -0.048  0.047 -0.009  0.047  0.123 -0.144 -0.048 -0.151 -0.126       
Unknown     -0.045  0.044  0.127  0.095  0.020 -0.051 -0.054 -0.013 -0.054 -0.127
AIC(lm_mod_log)
[1] 1906.818

plot(lm_mod_log)
shapiro.test(residuals(lm_mod_log))

    Shapiro-Wilk normality test

data:  residuals(lm_mod_log)
W = 0.99062, p-value = 1.592e-07

GAM

library(mgcv)
mod_gam = gam(colony_lost_pct ~ year + months + s(Varroa.mites,bs='tp') +Other.pests.parasites+Disesases+Pesticides+Other+Unknown + state, data = data)
summary(mod_gam)

Family: gaussian 
Link function: identity 

Formula:
colony_lost_pct ~ year + months + s(Varroa.mites, bs = "tp") + 
    Other.pests.parasites + Disesases + Pesticides + Other + 
    Unknown + state

Parametric coefficients:
                        Estimate Std. Error t value
(Intercept)            5.5260467  1.4847134   3.722
year                  -0.0026593  0.0007354  -3.616
monthsQ2              -0.0613768  0.0045969 -13.352
monthsQ3              -0.0415819  0.0048986  -8.489
monthsQ4              -0.0302073  0.0046885  -6.443
Other.pests.parasites -0.0459144  0.0187584  -2.448
Disesases              0.0175029  0.0291659   0.600
Pesticides             0.0061584  0.0231664   0.266
Other                  0.2535213  0.0293613   8.635
Unknown                0.1758598  0.0362995   4.845
statearizona           0.0169103  0.0156753   1.079
statearkansas         -0.0143230  0.0156305  -0.916
statecalifornia       -0.0511942  0.0158766  -3.224
statecolorado         -0.0110859  0.0159158  -0.697
stateconnecticut      -0.0617037  0.0158093  -3.903
stateflorida          -0.0320959  0.0156045  -2.057
stategeorgia          -0.0254979  0.0156614  -1.628
statehawaii           -0.0719185  0.0165875  -4.336
stateidaho            -0.0548765  0.0159085  -3.450
stateillinois         -0.0058733  0.0155178  -0.378
stateindiana          -0.0143542  0.0156826  -0.915
stateiowa             -0.0461383  0.0157033  -2.938
statekansas            0.0208066  0.0156416   1.330
statekentucky         -0.0161372  0.0153743  -1.050
statelouisiana        -0.0572221  0.0154701  -3.699
statemaine            -0.0382717  0.0158274  -2.418
statemaryland         -0.0085159  0.0156844  -0.543
statemassachusetts    -0.0172211  0.0156639  -1.099
statemichigan         -0.0397056  0.0157084  -2.528
stateminnesota        -0.0384881  0.0158745  -2.425
statemississippi      -0.0395693  0.0153712  -2.574
statemissouri         -0.0236265  0.0154902  -1.525
statemontana          -0.0835353  0.0157492  -5.304
statenebraska         -0.0372543  0.0158226  -2.354
statenew jersey       -0.0743590  0.0157899  -4.709
statenew mexico        0.0348459  0.0163957   2.125
statenew york         -0.0368258  0.0155991  -2.361
statenorth carolina   -0.0244718  0.0155362  -1.575
statenorth dakota     -0.0673175  0.0157752  -4.267
stateohio             -0.0170303  0.0154988  -1.099
stateoklahoma         -0.0346881  0.0157300  -2.205
stateoregon           -0.0772707  0.0158699  -4.869
stateother states     -0.0201813  0.0158388  -1.274
statepennsylvania     -0.0224632  0.0156617  -1.434
statesouth carolina   -0.0337539  0.0154904  -2.179
statesouth dakota     -0.0663129  0.0158477  -4.184
statetennessee         0.0071402  0.0153367   0.466
statetexas            -0.0469480  0.0155199  -3.025
stateutah             -0.0312697  0.0158357  -1.975
statevermont          -0.0725679  0.0158225  -4.586
statevirginia         -0.0200102  0.0154137  -1.298
statewashington       -0.0512636  0.0158557  -3.233
statewest virginia    -0.0236389  0.0156273  -1.513
statewisconsin        -0.0439683  0.0157134  -2.798
statewyoming          -0.0331200  0.0159010  -2.083
                      Pr(>|t|)    
(Intercept)           0.000206 ***
year                  0.000311 ***
monthsQ2               < 2e-16 ***
monthsQ3               < 2e-16 ***
monthsQ4              1.66e-10 ***
Other.pests.parasites 0.014512 *  
Disesases             0.548536    
Pesticides            0.790410    
Other                  < 2e-16 ***
Unknown               1.42e-06 ***
statearizona          0.280885    
statearkansas         0.359656    
statecalifornia       0.001294 ** 
statecolorado         0.486221    
stateconnecticut      1.00e-04 ***
stateflorida          0.039906 *  
stategeorgia          0.103756    
statehawaii           1.57e-05 ***
stateidaho            0.000580 ***
stateillinois         0.705131    
stateindiana          0.360211    
stateiowa             0.003361 ** 
statekansas           0.183688    
statekentucky         0.294091    
statelouisiana        0.000226 ***
statemaine            0.015743 *  
statemaryland         0.587259    
statemassachusetts    0.271797    
statemichigan         0.011603 *  
stateminnesota        0.015467 *  
statemississippi      0.010158 *  
statemissouri         0.127444    
statemontana          1.33e-07 ***
statenebraska         0.018699 *  
statenew jersey       2.76e-06 ***
statenew mexico       0.033753 *  
statenew york         0.018387 *  
statenorth carolina   0.115470    
statenorth dakota     2.12e-05 ***
stateohio             0.272056    
stateoklahoma         0.027617 *  
stateoregon           1.26e-06 ***
stateother states     0.202836    
statepennsylvania     0.151739    
statesouth carolina   0.029513 *  
statesouth dakota     3.06e-05 ***
statetennessee        0.641609    
statetexas            0.002536 ** 
stateutah             0.048525 *  
statevermont          4.95e-06 ***
statevirginia         0.194450    
statewashington       0.001256 ** 
statewest virginia    0.130612    
statewisconsin        0.005217 ** 
statewyoming          0.037460 *  
---
Signif. codes:  
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Approximate significance of smooth terms:
                  edf Ref.df     F p-value    
s(Varroa.mites) 4.191  5.204 10.34  <2e-16 ***
---
Signif. codes:  
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

R-sq.(adj) =   0.37   Deviance explained = 39.8%
GCV = 0.0035351  Scale est. = 0.0033783  n = 1334
gam::plot.Gam(mod_gam, se=TRUE)
---
title: "Regression"
output: html_notebook
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
knitr::opts_knit$set(root.dir = "/Users/lucamainini/Documents/GitHub/np_project/")
```

```{r import data}
library(readr)
data <- read_csv("data/new_data/data_bystate_temp_perc.csv")
```

```{r}
library(dplyr)
data <- data %>% mutate(colony_lost_pct = colony_lost_pct/100)
data <- data %>% mutate(Varroa.mites = Varroa.mites/100)
data <- data %>% mutate(Other.pests.parasites = Other.pests.parasites/100)
data <- data %>% mutate(Disesases = Disesases/100)
data <- data %>% mutate(Pesticides = Pesticides/100)
data <- data %>% mutate(Other = Other/100)
data <- data %>% mutate(Unknown = Unknown/100)
```

## LINEAR MODEL

```{r}
lin_mod_n <- lm(data=data, colony_lost ~ colony_max + state + months + Varroa.mites +Other.pests.parasites+Disesases+Pesticides+Other+Unknown+year)
summary(lin_mod_n)
```

```{r}
lin_mod <- lm(data=data, colony_lost_pct ~ state + months + Varroa.mites +Other.pests.parasites+Disesases+Pesticides+Other+Unknown)
summary(lin_mod)
```

```{r}
library(car)
b <- coefficients(lin_mod)
e <- residuals(lin_mod)

cat("Verify the hypothesis:\n")
par(mfrow=c(2,2))
plot(lin_mod)


par(mfrow=c(1,1))
cat("Verify normality of residuals:\n")
shapiro.test(residuals(lin_mod))
shapiro.test(rstudent(lin_mod))

cat("VIF:\n")
vif(lin_mod)
```

Le ipotesi del modello lineare non sono verificate.

## LOGIT

Non so se logit va bene visto che abbiamo valori nell'intervallo 0-1 e non 0,1.

```{r}
data = data %>% mutate(logit_colony_lost_pct=logit(colony_lost_pct))
```

```{r}
logit_mod <- lm(data=data, logit_colony_lost_pct ~ state + months + Varroa.mites +Other.pests.parasites+Disesases+Pesticides+Other+Unknown)
summary(logit_mod)

AIC(logit_mod)

cat("Verify the hypothesis:\n")
par(mfrow=c(2,2))
plot(logit_mod)


par(mfrow=c(1,1))
cat("Verify normality of residuals:\n")
shapiro.test(residuals(logit_mod))
shapiro.test(rstudent(logit_mod))

cat("VIF:\n")
vif(logit_mod)
```

```{r}
library(outliers)
x = outlierTest(logit_mod)
x
```

```{r}
data_without_outliers = data[-c(897,921),]

logit_mod <- lm(data=data_without_outliers, logit_colony_lost_pct ~ state + months + Varroa.mites +Other.pests.parasites+Disesases+Pesticides+Other+Unknown)
summary(logit_mod)

AIC(logit_mod)

cat("Verify the hypothesis:\n")
par(mfrow=c(2,2))
plot(logit_mod)


par(mfrow=c(1,1))
cat("Verify normality of residuals:\n")
shapiro.test(residuals(logit_mod))
shapiro.test(rstudent(logit_mod))

cat("VIF:\n")
vif(logit_mod)
```

```{r}
# GLM NON DA USARE
logit_mod <- glm(colony_lost_pct ~ months + state + Varroa.mites +Other.pests.parasites+Disesases+Pesticides+Other+Unknown,
                  data = data,family = "binomial")
summary(logit_mod)

AIC(logit_mod)

cat("Verify the hypothesis:\n")
par(mfrow=c(2,2))
plot(logit_mod)


par(mfrow=c(1,1))
cat("Verify normality of residuals:\n")
shapiro.test(residuals(logit_mod))
shapiro.test(rstudent(logit_mod))

cat("VIF:\n")
vif(logit_mod)
```

# BETA REGRESSION

```{r}
require(betareg)
beta_mod <- betareg(colony_lost_pct ~ months + Varroa.mites + Other.pests.parasites+Disesases+Pesticides+Other+Unknown + state,
                  data = data)
summary(beta_mod)
AIC(beta_mod)
```

# Linear Mixed Models

```{r}
library(lme4)
lm_mod <- lmer(colony_lost_pct ~ year + months + Varroa.mites +Other.pests.parasites+Disesases+Pesticides+Other+Unknown + (1|state),
                  data = data)
summary(lm_mod)
AIC(lm_mod)
```

```{r}
fm16.1mer = lm_mod
plot(fm16.1mer)
shapiro.test(residuals(fm16.1mer))
```

```{r}
library(lme4)
library(insight)
confint(fm16.1mer,oldNames=TRUE)

## Var-Cov matrix of fixed-effects
vcovb <- vcov(fm16.1mer) 
cat("\nVar-Cov matrix of fixed-effects:\n")
vcovb
corb <- cov2cor(vcovb) 
nms <- abbreviate(names(fixef(fm16.1mer)), 5)
rownames(corb) <- nms
cat("\nCorrelation matrix of fixed-effects:\n")
corb

cat("Var-Cov matrix of random-effects and errors\n")
print(vc <- VarCorr(fm16.1mer), comp = c("Variance", "Std.Dev."))

sigma2_eps <- as.numeric(get_variance_residual(fm16.1mer))
cat("the variance associated to eps sigma2_eps is",sigma2_eps)
sigma2_b <- as.numeric(get_variance_random(fm16.1mer))
cat("the variance associated to random effect sigma2_b is",sigma2_b)

## Let's compute the conditional and marginal var-cov matrix of Y
sgma <- summary(fm16.1mer)$sigma  # sigma^2

A <- getME(fm16.1mer, "A") # A  --> N x n, A represents the D (not italic), variance of random effect
I.n <- Diagonal(ncol(A)) # IN  --> n x n

## the conditional variance-covariance matrix of Y (diagonal matrix)
## conditional to the random effect è semplicemente la matrice fixed effect
cat("\n SigmaErr:\n")
SigmaErr = sgma^2 * (I.n)
# SigmaErr ha dimensione n_oss x n_oss

# Conditioned to the random effects b_i, we observe the var-cov of the errors
# that are independent and homoscedastic

## we visualize the first 20 rows/columns of the matrix
plot(as.matrix(SigmaErr[1:20,1:20]), main = 'Conditional estimated Var-Cov matrix of Y')

cat("the MARGINAL variance-covariance matrix of Y (block-diagonal matrix) is")
V <- sgma^2 * (I.n + crossprod(A)) # V = s^2*(I_N+A*A) --> s^2*(I_N) is the error part, s^2*(A*A) is the random effect part
  #-> V is a block-diagional matrix, the marginal var-cov matrix

# visualization of the first 20 rows/columns
plot(as.matrix(V[1:20,1:20]), main = 'Marginal estimated Var-Cov matrix of Y')


# Another way to interpret the variance output is to note percentage of the subject variance out 
# of the total, i.e. the Percentage of Variance explained by the Random Effect (PVRE).
# This is also called the intraclass correlation (ICC), because it is also an estimate of the within 
# cluster correlation.

PVRE <- sigma2_b/(sigma2_b+sigma2_eps)
cat("The Proportion of Variance due to Random Effect is",PVRE) # 15% is quite high! 

cat("\nvisualization of the random intercepts with their 95% confidence intervals in the dotplot\n")
# Random effects: b_0i for i=1,...,234
dotplot(ranef(fm16.1mer, condVar=T))
```

```{r}
library(plotly)
x = ranef(fm16.1mer, condVar=T)
us_data <- map_data("state")
df <- data.frame(
  state = tolower(rownames(x$state)),
  values = x$state$`(Intercept)`
)
library(usmap)
plot_usmap(data = df) + labs(title = "Cluster by prec")
```

```{r}
# 1) Assessing Assumption on the within-group errors
#it's just a sample from the entire population, so to take with care

plot(fm16.1mer)  ## Pearson and raw residuals are the same now

qqnorm(resid(fm16.1mer))
qqline(resid(fm16.1mer), col='red', lwd=2)
shapiro.test(resid(fm16.1mer))

# 2) Assessing Assumption on the Random Effects

qqnorm(unlist(ranef(fm16.1mer)$state), main='Normal Q-Q Plot - Random Effects on Intercept')
qqline(unlist(ranef(fm16.1mer)$state), col='red', lwd=2)
shapiro.test(unlist(ranef(fm16.1mer)$state))

AIC(fm16.1mer)
```

```{r}
lm_mod_log <- lmer(logit_colony_lost_pct ~ year + months + Varroa.mites +Other.pests.parasites+Disesases+Pesticides+Other+Unknown + (1|state),
                  data = data)
summary(lm_mod_log)
AIC(lm_mod_log)
```
```{r}
plot(lm_mod_log)
shapiro.test(residuals(lm_mod_log))
```

## GAM

```{r}
library(mgcv)
mod_gam = gam(colony_lost_pct ~ year + months + s(Varroa.mites,bs='tp') +Other.pests.parasites+Disesases+Pesticides+Other+Unknown + state, data = data)
summary(mod_gam)
```
```{r}
gam::plot.Gam(mod_gam, se=TRUE)
```

